DOCSLIB.ORG

Physics Chapter 9

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Physics Chapter 9 5. In Figure 10 of this section, ray 1 is incident on the inside surface of the glass fibre at an angle less than the critical angle. (a) What is the critical angle for this fibre if the index of refrac- tion for the glass is 1.50? (b) With what maximum angle relative to the normal of the fibre’s end can it strike the end of the fibre without later escaping? Applying Inquiry Skills 6. Design an experiment to determine whether light will undergo DID YOU KNOW ? total internal reflection within gases, for example, when travelling ϭ ϭ Medical Application of Total in carbon dioxide (n 1.000450) toward air (n 1.000293). What Internal Reflection is the critical angle of light in carbon dioxide, according to Snell’s law? How will this affect the design of your experiment? An endoscope is a device that transmits images using bundles of fibres. Endoscopes Making Connections probe parts of the body that would otherwise 7. Research which fields, other than communications, have been require exploratory surgery. greatly affected by the use of fibre optics. 9.7 Applications of Refraction Geometric optics is a good model of light for explaining many natural optical phenomena. Recall that a point is perceived by the eye when a cone of diverging light enters the eye. The diverging light is traced backward and where the rays meet, an image of the object is perceived. Atmospheric Refraction For many purposes, we assume the index of refraction of air to be 1.000. Although variation of the index of refraction of air from this value is just a small fraction of a percent, it is this small fraction that causes many optical effects. The atmosphere’s index of refraction varies, especially along vertical lines. Refractive effects such as mirages and shimmering are due to variations in the index of refraction caused by temperature variations. Twinkling and Shimmering DID YOU KNOW ? Earth’s atmosphere consists of flowing masses of air of varying density and tem- perature; therefore, the refractive index varies slightly from one region of the Observing the Sky atmosphere to another. When light from a star enters the atmosphere it is Most large telescopes are located high on refracted as it moves from one mass of air to another, and, since the variable mountains where there is less of Earth’s masses of air are in motion, the star seems to twinkle. atmosphere between them and the stars, and Under conditions of constant pressure, warm air has a slightly lower index where the air is more uniform in temperature. of refraction than cold air. When light passes through a stream of warm air, as it This minimizes distortions caused by atmos- does above a hot stove or barbecue, it is refracted away from the normal. This pheric refraction. Astronomers find that cold refraction is not uniform because the warm air rises irregularly, in gusts. Light winter nights are usually best for celestial observation since vertical temperature varia- from objects seen through the warm air is distorted by irregular refraction, and tions are minimized. Any atmospheric distor- the objects appear to shimmer. You can see the same effect over hot pavement in tions are corrected using specialized software. the summer or at an airport as jets go by. 346 Chapter 9 9.7 Mirages Two types of mirages can occur, depending on the temperature variation. An inferior mirage occurs when cooler layers of air lie above warmer layers. The viewer sees an image displaced downward. Inferior mirages are most often asso- ciated with deserts, but can occur over any hot, flat surface, such as a road on a summer day (Figure 1). As the light from the sky nears the ground it is progres- sively refracted by successive layers of warmer air, each with a lower index of refraction (Figure 2). The angle of incidence to the boundaries of these layers keeps increasing. Eventually, the light is totally internally reflected upward from one of the layers. What your eye sees is a virtual image of the sky below the road. It just appears that there is a layer of water on the road because you perceive that there is a reflecting surface. objectdirect light through air of uniform refracted index eye Figure 1 cool air Sometimes, what seems to be a sheet of warm air hot air water appears on the highway a short dis- tance ahead of you, but you never reach it. hot flat pavement image Figure 2 An inferior mirage A superior mirage occurs when optically denser layers of air lie below less dense layers. The viewer sees an image displaced upward, as in Figure 3(a). In this case, light refracts toward the denser air (Figure 3(b)). (a) Figure 3 (a) A complex mirage of the Alaska Range with Mt. McKinley on the far right, (b) less dense air 250 km away. In this photograph there image are no clouds. This mirage is a result of a temperature inversion: layers of cold air lie beneath layers of warmer air. more dense air (b) Light refracts toward denser air. A virtual eye object image is perceived. Light Rays, Reflection, and Refraction 347 When the Sun is very close to the horizon, the light from the lower part of the Sun is refracted more than the light from the upper part (Figure 4). This gives the impression that the Sun has a flattened bottom, making it appear oval rather than round. Try This Activity Mirages A mirage can be set up in a laboratory setting using solutions of dif- Figure 4 ferent densities and an empty fish tank. The shape of the Sun appears to change as it Materials: a fish tank, solutions with different densities, and a simple approaches the horizon. line drawing. • Pour the densest solution into the fish tank first. • To prevent mixing, pour the second solution slowly onto a board that is placed on the first solution. The second solution will float on top of the denser first solution. • At the end of the fish tank place a simple line drawing. Look at the drawing through the other end of the fish tank. Compare what you see through the fish tank with what you see at the same distance dispersion: the spreading of white light without the fish tank in place. into a spectrum of colours • Repeat the previous two steps by adding a third liquid, less dense than the other two. (a) If you see a mirage, is it an inferior or superior mirage? Explain. • Demonstrate the device to your class. Dispersion and Rainbows The ancient Egyptians were probably the first to discover that fragments of clear, colourless glass and precious stones spread, or disperse, the colours of the rainbow when placed in the path of a beam of white light. We now know that the index of refraction of a medium changes according to the colour of light that is entering the medium. These changes in the index of refraction are the source of dispersion. A rainbow is the Sun’s spectrum produced by water droplets in the atmos- Figure 5 phere (Figure 5). Light enters the spherical rain droplets, where it is refracted, This photograph shows a rainbow over the onetime home of Sir Isaac Newton. When dispersed, and reflected internally. The violet and red rays intersect internally, watching the dazzling colours of a rainbow, emerging with violet at the top, red at the bottom, and the other colours of the you likely make two basic observations. First, spectrum in between. If the rays that enter your eye are traced backward, you can rainbows consist of the same colours of the see an image called the primary rainbow (Figure 6). Other orders of rainbows, spectrum as produced by a prism, with red on which are much more difficult to observe than a primary rainbow, occur when the outside of the bow and blue and violet on the light is internally reflected more than once. For instance, a secondary the inside. Second, whenever you see a rainbow, which is located higher in the sky than the primary (Figure 5), occurs rainbow, the Sun is at your back. This is why after two internal reflections. you see rainbows in the western sky in the morning and in the eastern sky before sunset. A rainbow arc appears at certain points in the sky because droplets of water Both of these observations can be explained along that arc reflect the spectrum at just the right angle into the eye of the by the concepts of dispersion, refraction, and observer. The angle is approximately 42° to the horizontal sunlight. total internal reflection. primary rainbow: the rainbow of visible spectral colours that results from a single internal reflection in rain drops 348 Chapter 9 9.7 sunlight 42° water droplets 40° Figure 6 Formation of a primary rainbow. Looking at millions of drops, you see the spectrum in an arc of a semicircle with red on the outside and violet on the inside. Activity 9.7.1 Modelling Atmospheric Refraction There is a continuous decrease in the index of refraction of air as you move from the ground to the outermost layer of the atmosphere. Although the decrease in temperature increases the index of refraction, the decrease in pressure as you move up through the atmosphere has a greater effect on the index of refraction. This effect is simplified by representing the atmosphere by layers (Figure 7). Figure 7 1 The indexes of refraction of the layers of the atmosphere. (Layers not to scale.) 2 n = 1.0000 exosphere n = 1.000 024 thermosphere n = 1.000 026 mesosphere n = 1.000 028 stratosphere n = 1.000 03 tropopause and troposphere ground actual light observer from the Sun Procedure 1.
Load more

Recommended publications
  • Atmospheric Optics
    53 Atmospheric Optics Craig F. Bohren Pennsylvania State University, Department of Meteorology, University Park, Pennsylvania, USA Phone: (814) 466-6264; Fax: (814) 865-3663; e-mail: [email protected] Abstract Colors of the sky and colored displays in the sky are mostly a consequence of selective scattering by molecules or particles, absorption usually being irrelevant. Molecular scattering selective by wavelength – incident sunlight of some wavelengths being scattered more than others – but the same in any direction at all wavelengths gives rise to the blue of the sky and the red of sunsets and sunrises. Scattering by particles selective by direction – different in different directions at a given wavelength – gives rise to rainbows, coronas, iridescent clouds, the glory, sun dogs, halos, and other ice-crystal displays. The size distribution of these particles and their shapes determine what is observed, water droplets and ice crystals, for example, resulting in distinct displays. To understand the variation and color and brightness of the sky as well as the brightness of clouds requires coming to grips with multiple scattering: scatterers in an ensemble are illuminated by incident sunlight and by the scattered light from each other. The optical properties of an ensemble are not necessarily those of its individual members. Mirages are a consequence of the spatial variation of coherent scattering (refraction) by air molecules, whereas the green flash owes its existence to both coherent scattering by molecules and incoherent scattering
    [Show full text]
  • Einstein's Mirage
    Paul L. Schechter Einstein’s Mirage he first prediction of Einstein’s general theoryof relativity T to be verified experimentallywas the deflection of light by a massive body—the Sun. In weak gravitational fields (and for such purposes the Sun’s field is considered weak), light behaves as if there were an index of refraction proportional to the gravitational potential. The stronger the gravitational field, the larger the angu- lar deflection of the light. The Sun is not unique in this regard, and it was quickly appreci- ated that stars in our own galaxy (the MilkyWay) and the combined mass of stars in other galaxies would also, on very rare occasions, produce observable deflections. Variations in the “gravitational” index of refraction would also distort images, stretching them in some directions and shrinking them in others. In the analogous case of terrestrial mirages, the deflections and distortions are due to thermal variations in the index of refraction of air. 36 ) schechter mit physics annual 2003 OTH TERRESTRIAL AND GRAVITATIONAL Bmirages sometimes produce multiple distorted images of the same object. When they do, at least one of the images has the opposite handedness of the object being imaged—it is a mirror image, but distorted. At least one of the other images must have the correct handedness, but it will also be distorted. The French call such distorted images gravitational mirages. In the half century following the confirmation of general relativity, the idea that cosmic mirages might actually be observed was taken seriously byonly a small number of astrophysicists. Most of the papers written on the subject treated them as academic curiosities, far too unlikely to actually be observed.
    [Show full text]
  • Superior Mirage: Aesthetic Recollections of the Great Lakes
    Rochester Institute of Technology RIT Scholar Works Theses 12-2014 Superior Mirage: Aesthetic Recollections of the Great Lakes S Caswell Follow this and additional works at: https://scholarworks.rit.edu/theses Recommended Citation Caswell, S, "Superior Mirage: Aesthetic Recollections of the Great Lakes" (2014). Thesis. Rochester Institute of Technology. Accessed from This Thesis is brought to you for free and open access by RIT Scholar Works. It has been accepted for inclusion in Theses by an authorized administrator of RIT Scholar Works. For more information, please contact [email protected]. Superior Mirage {Aesthetic Recollections of the Great Lakes} By S. Caswell December 2014 A Thesis Submitted in Candidacy for the Degree of Master of Fine Arts-Fine Arts Studio School of Art College of Imaging Arts and Sciences Rochester Institute of Technology Rochester, N.Y. Thesis Approval Superior Mirage By S. Caswell Dr. Tom Lightfoot Date Committee Chair Professor Luvon Sheppard Date Committee Member Professor Elizabeth Kronfield Date Committee Member Acknowledgements I would like to thank the committee of Dr. Tom Lightfoot, Prof. Luvon Sheppard, and Prof. Elizabeth Kronfield for their inspiration, guidance and support in the fruition of this thesis work. Each of your guidance has propelled my work to a higher level due to your individual input and depth of knowledge both artistically and intellectually. This is also the place to thank those who mentored me at Roberts Wesleyan College who were monumental in shaping the way I see as an artist. Thank you to Prof. Scot Bennett, Prof. Douglas Giebel, Prof. Jill Kepler, and Prof Alice Drew.
    [Show full text]
  • Analysis of an Infrared Mirage Sequence
    Analysis of an infrared mirage sequence Waldemar H. Lehn Infrared observations of seaborne thermal sources are subject to the effects of atmospheric refraction. For low elevation angles at long ranges, out to the limit of visibility, the inevitable atmospheric temper- ature gradients frequently produce mirages. I present an analysis of a 22-min sequence of images recorded on 18 February 1994 at the U.S. Naval Surface Warfare Center at Wallops Island, Virginia. The infrared target is a heat source carried on a ship moving in a straight line toward the camera. The images show a quasi-periodic variation of the horizon elevation, as well as an extended range of visibility. A model that reasonably reproduces the observed features consists of a small temperature inversion in a slightly sloped atmosphere, with an atmospheric gravity wave moving across the line of sight. © 1997 Optical Society of America Key words: Infrared mirage, atmospheric refraction. 1. Introduction ~i! parallel to shore at a nominal bearing angle of 199° All long-range optical observations are affected by toward a fixed station, where the target was a heat refraction in the atmosphere. A well-known exam- source that could be moved up or down a mast ~ele- ple is astronomical refraction that creates a small vations 4.4–26.6 m above mean sea level! and ~ii! apparent vertical displacement of a star or distant directly out to sea at nominal bearing 130°, observing object. Refraction within the surface layer, how- a heat source target on a ship sailing directly toward ever, is not always uniform and on occasion can cause or away from the test site, with two possible target considerable distortion.
    [Show full text]
  • Mirage in Geometrical Optics and the Horizontal Ray
    STUDENT JOURNAL OF PHYSICS Mirage in geometrical optics and the horizontal ray Dhiman Biswas1 ,∗ Simran Chourasia2 ,y Rathindra Nath Das1 ,z Rajesh B. Khaparde3 ,x Ajit M. Srivastava4 { 1. B.Sc. final year, Ramakrishna Mission Residential College Narendrapur, Kolkata - 700103 2. M.Sc. 3rd year, National Institute of Science Education and Research, Bhubaneswar 3. Homi Bhabha Centre for Science Education, TIFR, Mankhurd, MUMBAI – 400088 4. Institute of Physics, Bhubaneswar 751005 Abstract. Mirage forms when light rays traversing a medium with spatially varying refractive index bend and undergo total internal reflection. Typical example is when downward going light rays bend upward when heated air in contact with hot earth surface leads to vertical gradient of refractive index with refractive index increasing in upward direction. A conceptual issue arises when considering the part of the light trajectory where light ray becomes horizontal. With refractive index varying only in the vertical direction, one will expect from symmetry considerations that a horizontal ray should not bend, contrary to the observed phenomenon of mirage. This issue has been discussed in literature, e.g. by Raman and Pancharatnam and by Berry. We discuss their arguments and argue that there are subtle conceptual issues in understanding mirage strictly in the framework of geometrical optics. In particular, we consider a horizontally moving light ray and argue that within geometrical optics, such a ray should continue to move horizontally. Bending of such a ray, as required by the mirage phenomenon, must require considerations of wave nature of light. Keywords: Mirage, geometrical optics, wave optics, Fermat’s principle, horizontal ray 1.
    [Show full text]
  • Atmospheric Refraction: a History
    Atmospheric refraction: a history Waldemar H. Lehn and Siebren van der Werf We trace the history of atmospheric refraction from the ancient Greeks up to the time of Kepler. The concept that the atmosphere could refract light entered Western science in the second century B.C. Ptolemy, 300 years later, produced the first clearly defined atmospheric model, containing air of uniform density up to a sharp upper transition to the ether, at which the refraction occurred. Alhazen and Witelo transmitted his knowledge to medieval Europe. The first accurate measurements were made by Tycho Brahe in the 16th century. Finally, Kepler, who was aware of unusually strong refractions, used the Ptolemaic model to explain the first documented and recognized mirage (the Novaya Zemlya effect). © 2005 Optical Society of America OCIS codes: 000.2850, 010.4030. 1. Introduction the term catoptrics became reserved for reflection Atmospheric refraction, which is responsible for both only, and the term dioptrics was adopted to describe astronomical refraction and mirages, is a subject that the study of refraction.2 The latter name was still in is widely dispersed through the literature, with very use in Kepler’s time. few works dedicated entirely to its exposition. The same must be said for the history of refraction. Ele- ments of the history are scattered throughout numer- 2. Early Greek Theories ous references, many of which are obscure and not Aristotle (384–322 BC) was one of the first philoso- readily available. It is our objective to summarize in phers to write about vision. He considered that a one place the development of the concept of atmo- transparent medium such as air or water was essen- spheric refraction from Greek antiquity to the time of tial to transmit information to the eye, and that vi- Kepler, and its use to explain the first widely known sion in a vacuum would be impossible.
    [Show full text]
  • Sweet Mirage
    Sweet Mirage Adam Benslama Princeton High School March 07, 2021 Abstract A simple experiment is presented to replicate the Fata Morgana effect in the laboratory. A quantitative analysis is done using ray tracing with both photographic and mathematical tech- niques. The mirage's image, as seen by the eye or the camera lens, can be used to analyze the bending of light rays as well as the distortion of the mirage's image. Introduction ferent temperatures [3], or mixable liquids of different densities [4] [5]. The key point for these types of experiments to be effective is to A mirage is a marvelous natural optical phe- achieve a stable enough refractive index gradi- nomenon. Thermal gradients in the atmo- ent. As a consequence, a well defined pattern sphere and the associated refractive index of light rays will be produced. changes make light rays bend. An object can be seen in a higher or lower position than it In this paper, we present a simple way to repli- actually is, creating an optical illusion. For cate the Fanta Morgana effect in the labora- example, on a hot summer day, one may per- tory. Our setup shows a detailed structure of ceive what appears to be puddles of water on the mirage with the corresponding behavior of a hot distant road, on which we perceive what light rays to be observed. We also discuss a ray appears to be the reflections of other objects. tracing procedure we used to qualitatively re- Another example is the Fata Morgana effect construct the mirage. We used a camera with [1] which is a type of superior mirage by which a known field of view and a transparent con- distant objects appear inverted, distorted, dis- tainer to consistently take pictures of the con- placed or multiplied.
    [Show full text]
  • Sugar Water Mirage
    Light Touch Sugar WaterMirage The thin blanket of air that envelopes the Earth is rarefied at high altitudes blue and densifies with proximity to the surface. Thus the refractive index of the atmosphere increases in a continuous manner from unity in the vacuum of space to approximately n=1.000293 at sea level (h=0.5893 prn). Everywhere the gradient of the refractive index points toward the Earth's center, and so light passing from the sun to an observer on Earth will take straight or curved paths F~QURE1. (a) AN OBSERVER CAN SEE depending on whether the light DIRECT SUNLIGHT (SOLIDLINE) EVEN travels parallel or perpendicular to WHEN A STRAIGHT RAY PATH (DASHED the index gradient. At high noon, the LINE) IS BLOCKED; (b) DURING A LUNAR direct sunlight observed from the ECLIPSE, SOME LIGHT IS LENSED ground travels through the atmo- AROUND THE EARTHAND DIMLY . sphere along a straight trajectory. ILLUMINATES THE MOON; <C) THE 2a Direct sunlight reaching us at sunrise FLATTENING OF TM,E SUN'S DISK OCCURS warm or sunset has taken a curved path, WHEN THE SUN IS LOW IN THE SKY. bending toward the hgh refractive blGHT FROM POINT A IS BENT SO AS TO index layers near the ground. APPEAR TO BE COMING FROM POINT B. The curved ray trajectory at sunrise or sunset leads to a variety of sight is the flattening of the sun's interesting effects. For example, we disk at sunrise or sunset. Again, the can see direct sunlight when the sun appearance is the result of curved ray is behind the Earth in the moments paths along the Earth's atmosphere before sunrise and after sunset (see (see Fig.
    [Show full text]
  • Road Surface Mirage: a Bunch of Hot Air?
    Article Optics April 2011 Vol.56 No.10: 962–968 doi: 10.1007/s11434-011-4347-9 SPECIAL TOPICS: Road surface mirage: A bunch of hot air? ZHOU HuaiChun1*, HUANG ZhiFeng1,2, CHENG Qiang1, LÜ Wei1, QIU Kui1, CHEN Chen1 & HSU Pei-feng2 1 State Key Laboratory of Coal Combustion, School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan 430074, China; 2 Department of Mechanical and Aerospace Engineering, Florida Institute of Technology, Melbourne, FL 32901-6975, USA Received September 25, 2010; accepted November 14, 2010 The inferior mirage from road surfaces is a common phenomenon, which can be easily seen in everyday life. It has been recog- nized in the literature as a light refraction phenomenon due to the refractive index gradient caused by the temperature gradient in the air strata above the road surfaces. However, it was also suggested that the mirage is just a phenomenon of specular reflection at grazing incidence. Because of the lack of reasonable and quantitative evidence, the generally accepted light refraction theory has not yet been refuted. Here we show some mirror-like reflection images captured from a road surface stretch in Yujiashan North Road, Wuhan, China, when there was no obvious temperature gradient on or above the road, measured on a winter day in December 2009. This provided direct evidence to doubt the temperature induced light refraction mechanism of the inferior mirage. Furthermore, the critical grazing angle of about 0.2° to the road plane where the mirror-like reflection appears could not make the rough surface scatter incident light as a smooth surface according to the Rayleigh criterion.
    [Show full text]
  • 1911-12.] the Fata Morgana. 175
    1911-12.] The Fata Morgana. 175 XV.—The Fata Morgana. By Professor F. A. Forel, Morges, Switzerland. Abstract of an Address delivered before the Society on July II,., 1911; translated by Professor C. G. Knott. AMONG optical phenomena which originate over the surface of water there is one so ill-defined and ill-observed as to be still mysterious; till now it has received no valid explanation. The Italians call it the Fata Morgana. Under conditions still lacking precise description, there appear on the far side of the Straits of Messina certain fantastic visions, fortresses and castles of unknown cities, which seem to emerge from the sea, soon to vanish again. These are the "palaces" of the "fairy Morgana," which appear and dis- appear at the capricious stroke of the magician's wand. Most of the accounts of the phenomenon are founded on the extravagant description and the amazing picture published in 1773 by the Dominican friar Don Antonio Minasi, professor of botany at the Roman College of Sapienzia. This drawing, with its incoherent groupings of castles and boats, reflected and refracted at random in a manner quite inconsistent with physical possibilities, was largely the creation of the distorted imagination of an artist who did not understand in the least the wonderful illusion. To appreciate the confusion which reigns in the scientific world in regard to this phenomenon, the reader need only refer to the chapter on the Fata Morgana in Pernter's admirable work on Meteorological Optics (Vienna, 1910). There he will be impressed with the uncertainty of the conclusions reached by the author after a study of the insufficient and contradictory documents to which he had access.
    [Show full text]
  • Road Mirage Angle
    IOP Physics Education Phys. Educ. 54 P A P ER Phys. Educ. 54 (2019) 065009 (9pp) iopscience.org/ped 2019 Road mirage angle © 2019 IOP Publishing Ltd Michael J Ruiz PHEDA7 Department of Physics, University of North Carolina at Asheville, Asheville, NC 28804, United States of America 065009 E­mail: [email protected] M J Ruiz Abstract Road mirage angle A video is taken of a road­sign mirage from the passenger seat in a car traveling at constant speed on a highway. The video spans the duration of seeing the mirage of the sign, viewing the vanishing of the mirage as the car Printed in the UK approaches, and passing the road sign. The mirage angle, defined as the angle with respect to the horizontal at the moment the observer notes the vanishing of the mirage, can be determined from the video, the speed of the car, and PED known dimensions of the standard road sign. The value can be checked with a theoretical formula using the ambient weather temperament and consulting 10.1088/1361-6552/ab3c28 references to determine the temperature of the air in contact with the road surface. Agreement between observation and theory is within the error bounds. In the conclusion, a quick observational estimate is made in the car 1361­6552 without needing the video. Published Background water gives the desert traveler false hope of get­ When I was 10 years old in 1961 my family made ting a drink. 11 a trip by car from our home in Camden, New Over a body of water the temperature gra­ Jersey, USA to Beaufort, North Carolina, USA.
    [Show full text]
  • Image Transmission Under Arche Mirage Conditions by Waldemar H
    Image Transmission under Arche Mirage Conditions By Waldemar H. Lehn and H. Leonard Sawatzky' Summary: The arctic mirage, an optical effect fairly common in the high latitudes, occurs when the atmosphere exhibits qr eater-then-norrnul refractive capability. Light rays then follow paths concave toward th e earth, with curvature qr eater than or equal to that of the earth. The atmosphere acquires this refractive capability under conditions of temperature inversion, which exaggerate the fall-off of density (and hence refractive index) with elevation. Equations are presented that ca1culate density profile from any given temperature p rofi le : these results arc used to develop ru y path equations for nearly horizontal rays in the lower atmosphere. Ray paths are computed for two distinct mirage conditions (a strong sh al low inversion and a mild but deep inversion) as weIl as for th e standard atmosphere. With the aid of these paths, the appearance of th e environment is shown. The strong inversion produces the appearance of a seucer-shapcd earth (with image dtstortion near the horizon), whereas the mild inversion produces a "flat e arth" appearance that permits great viewing distances. Zusammenfassung: Die arktische Fata Morgana ist ein verhältnismäßig häufig vorkommender optischer Effekt in höheren Breiten, Er entsteht, wenn durch gesteigerte Densitätsschichtung der Atmosphäre Lichtstrahl­ bahnen gebrochen werden in einem Ausmaß, das der Krümmung der Erde gleicht oder sie überschreitet. Die Atmosphäre gewinnt diese Refraktionsfähigkeit unter Temperaturinversionsverhältnissen, welche die normale Densi tätsabnahrna mit zunehmender Höhe verstärken. Gleichungen, die das Densitätsprofil bei gegebenem Temperaturprofil errechnen lassen, werden vorgelegt. Aus den Ergebnissen lassen sich Behn-Gleidiunqen annähernd horizontaler Lichtstrahlen im bodennahen Raum entwickeln.
    [Show full text]